scholarly journals Boundary regularity of the solution to the complex Monge-Ampère equation on pseudoconvex domains of infinite type

2015 ◽  
Vol 22 (2) ◽  
pp. 467-484 ◽  
Author(s):  
Ly Kim Ha ◽  
Tran Vu Khanh
Keyword(s):  
Boundary Regularity ◽  
Pseudoconvex Domains ◽  
Infinite Type ◽  
Monge Ampere

Infinite type germs of real analytic pseudoconvex domains in ℂ3

2012 ◽  
Vol 57 (6) ◽  
pp. 705-717 ◽  
Author(s):  
John Erik Fornæss ◽  
Berit Stensønes
Keyword(s):  
Pseudoconvex Domains ◽  
Infinite Type ◽  
Real Analytic

scholarly journals Optimal boundary regularity for some singular Monge-Ampère equations on bounded convex domains

2021 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Nam Q. Le
Keyword(s):  
Boundary Data ◽  
Boundary Regularity ◽  
Hölder Regularity ◽  
Convex Domains ◽  
Open Convex ◽  
Optimal Boundary ◽  
Monge Ampere ◽  
Holder Regularity ◽  
Bounded Convex

<p style='text-indent:20px;'>By constructing explicit supersolutions, we obtain the optimal global Hölder regularity for several singular Monge-Ampère equations on general bounded open convex domains including those related to complete affine hyperbolic spheres, and proper affine hyperspheres. Our analysis reveals that certain singular-looking equations, such as <inline-formula><tex-math id="M1">\begin{document}$ \det D^2 u = |u|^{-n-2-k} (x\cdot Du -u)^{-k} $\end{document}</tex-math></inline-formula> with zero boundary data, have unexpected degenerate nature.</p>

scholarly journals Boundary regularity for the Monge–Ampère and affine maximal surface equations

2008 ◽  
Vol 167 (3) ◽  
pp. 993-1028 ◽  
Author(s):  
Neil Trudinger ◽  
Xu-Jia Wang
Keyword(s):  
Boundary Regularity ◽  
Maximal Surface ◽  
Monge Ampere
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